Quark-hadron phase transition in Brans-Dicke brane gravity

A standard picture in cosmology has been emerging over the past decade in which a phase transition, associated with chiral symmetry breaking after the electroweak transition, has occurred at approximately $10^{-6}$ seconds after the Big Bang to convert a plasma of free quarks and gluons into hadrons. In this paper, we consider the quark-hadron phase transition in a Brans-Dicke brane world scenario within an effective model of QCD. We study the evolution of the physical quantities relevant to quantitative description of the early universe, namely, the energy density, temperature and the scale factor before, during, and after the phase transition. We show that for different values of the Brans-Dicke coupling, $\omega$, phase transition occurs and results in decreasing the effective temperature of the quark-gluon plasma and of the hadronic fluid. We then move on to consider the quark-hadron transition in the smooth crossover regime at high and low temperatures and show that such a transition occurs and results in decreasing the effective temperature of the quark-gluon plasma during the process of quark-hadron phase transition.